rigid transformations and symmetry

Front

What is a rigid transformation?

Back

A transformation that preserves the shape and size of a figure, resulting in congruent figures.

Front

What are the three main types of rigid transformations?

Back

Translation, rotation, and reflection.

Front

Describe a rotation transformation.

Back

A transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle.

Front

What is the effect of a 180-degree rotation about the origin on a point (x, y)?

Back

The point is transformed to (-x, -y).

Front

What is a reflection transformation?

Back

A transformation that flips a figure over a line, creating a mirror image.

Front

How do you reflect a point (x, y) over the y-axis?

Back

The point is transformed to (-x, y).

Front

What is the rule for translating a point (x, y) by (a, b)?

Back

The new point is (x + a, y + b).

Front

What does it mean for figures to be congruent?

Back

Figures that have the same shape and size, but may be in different positions or orientations.

Front

Describe the reflection of a point (x, y) over the line y = x.

Back

The point is transformed to (y, x).

Front

What is the line of reflection in a reflection transformation?

Back

The line over which the figure is flipped to create a mirror image.